Saturday 24 October 2015

geometry - Overlapping circles. Distance to move 1 circle along specific line to remove overlap

I have two lines AB and CD that are not parallel.
There is a circle centered on each of points A and C.
The circles overlap as the distance between A and C is less than the two radii combined. The circles have the same radius.




To remove the overlap the circle at point C needs to be moved along the line towards D until the distance is greater than the radii of the circles.



I know the distance AC can be worked out which means I'd have:




  • the coordinates for both AB and CD

  • the distance AC, and the distance the center points need to be away from each other, radii of the circles.




The lines are almost but not quite parallel. Treating them as parallel (I've tried) doesn't produce accurate enough results. I don't know any of the angles.



How do I go from this information to moving the circle in line CD to coordinates on that line where the circles no longer overlap?

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